# Invariance properties of random curves: an approach based on integral geometry

@article{Mazzolo2020InvariancePO, title={Invariance properties of random curves: an approach based on integral geometry}, author={Alain Mazzolo}, journal={arXiv: Mathematical Physics}, year={2020} }

Traveled lengths statistic is a key quantity for characterizing stochastic processes in bounded domains. For straight lines and diffusive random walks, the average length of the trajectories through the domain is independent of the random walk characteristics and depends only on the ratio of the volume domain over its surface, a behavior that has been recently observed experimentally for exponential jump processes. In this article, based solely on geometrical concepts, we extend this remarkable…

## One Citation

### Mean arc theorem for exploring domains with randomly distributed arbitrary closed trajectories

- MathematicsThe European Physical Journal Plus
- 2022

A remarkable result from integral geometry is Cauchy’s formula, which relates the mean path length of ballistic trajectories randomly crossing a convex 2D domain, to the ratio between the region area…

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